3-D Separable-Denominator Digital Filters with Minimum L2-Sensitivity and No Overflow Oscillations

The problem of minimizing an L₂-sensitivity measure subject to L₂-norm dynamic-range scaling constraints for three-dimensional (3-D) separable-denominator digital filters is formulated. The constrained optimization problem is converted into an unconstrained optimization problem by using linear-algebraic techniques. Next, an efficient quasi-Newton algorithm is applied with closed-form formula for gradient evaluation to solve the unconstrained optimization problem. The optimal filter structure is then constructed by employing the resulting coordinate transformation matrix that minimizes the L₂-sensitivity measure subject to the scaling constraints. A numerical example is presented to illustrate the utility of the proposed technique